# Finding Distance from the Origin Given Velocity Graph

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1. Sep 18, 2016

### pocketofcandy

1. The problem statement, all variables and given/known data
A rocket-powered hockey puck move along a horizontal friction-less table. The figure (link posted below) shows the graphs of vx and vy, the x- and y- components of the puck's velocity. The puck starts at the origin. How far from the origin is the puck at 4 seconds?

Here is the picture of the two graphs: https://session.masteringphysics.com/problemAsset/1384028/7/4-9.jpg

[moderator's edit: Here's an inserted copy of the image just in case the link evaporates some day]

2. Relevant equations
area of a triangle: 1/2(b)(h)
area of a square: (l)(w)
sqrt(x2+y2)

3. The attempt at a solution
It appears on the on the vx graph that the velocity increases by an increment of 8 cm every second. (It is confirmed to be at 40 cm at 5 seconds). So I thought the way to do this would be to find the area under both graphs from 0 to 4 seconds.
On the vx graph, I found the area to be 1/2*4*32 = 64 cm. On the vy graph, I found the area to be 30*4 = 120 cm. Then I tried to use the formula for distance to solve and came out with:
sqrt(642 + 1202) = 136 cm.

However, whenever I put this answer in, it says it is incorrect. I guess I'm not really the best at physics, so I'm wondering where it was I made the error? I appreciate any help.

2. Sep 18, 2016

### Kaura

Strange as your answer seems to be correct at least from my judgement
I suppose make sure your answer is rounded correctly and that if required your answer is inputted with the correct units
Other than that I do not see an issue with your method
Maybe significant figures or something?

3. Sep 18, 2016

### pocketofcandy

Oh I see now that the site wants the answer to two significant figures. So that would be 1.4 meters then?

4. Sep 18, 2016

### Kaura

I believe so

5. Sep 18, 2016

### pocketofcandy

It worked that time. Thank you!

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